I always look at multiple sources from scholarly articles to government websites (and all of the in between) when doing research online. I sometimes find sources that present the same information and I am thinking it would be a good idea to back my writing up by using multiple references in my bibliography, to authenticate it. What do you think?
If you want to do it, go ahead. Like you said, it'll make your argument/results seem more credible because you have multiple sources backing you up.
In your bibliography, absolutely. If you are footnoting, I would only cite the most relevant source, except if I was quoting both (or several) sources on the same point in the text. This is often done when addressing something that is controversial or reaching a conclusion previously thought to be incorrect.
A pseudo-historian I learned to despise (and he is far from a lonely example) often treats different editions of a same book (or even translations to different languages!) as different sources - so his bibliography has more items, and he gets to "source" a faulty information or "base" a "conclussion" on seemingly different texts. Puke... Not that you're aiming for something like that but keep in mind that your reader might check on your sources, so make it clear that all of them share the same info. But stick to the one that you feel is more relevant...